establish the relation- v^2-u^2=2as, using velocity time graph....

Question

anonymous · Answer

solve plzz....

anonymous · Answer

...............................?????????????????

jamesj · Answer

Ok, so on a graph of velocity vs. time, what does the graph look like with constant acceleration a?

anonymous · Answer

yes

jamesj · Answer

What kinds of graphs can you have if acceleration a is a constant?

anonymous · Answer

velocity- time graph

jamesj · Answer

Yes, the y axis is velocity, and the x-axis is time.

What kinds of curves do we have for v as a function of t, v = v(t), if a is a constant?

Do we have just constant functions, i.e., horizontal lines?
Do we have straight lines in general?
Do we have parabolas?
Do we have other sorts of graphs?

anonymous · Answer

plzzzz do in ur way just/....

anonymous · Answer

????????????????????????????????????????????????

anonymous · Answer

plzzzzz fst

anonymous · Answer

@@JamesJ

jamesj · Answer

Look, can you answer my question?

jamesj · Answer

If a is a constant and u is the initial velocity, what is the formula for v, the final velocity?

v = .... what, as a function of u and t?

anonymous · Answer

v= u+at

jamesj · Answer

correct.  So in a velocity-time diagram, what kind of curve is that?

anonymous · Answer

straight curve

anonymous · Answer

i think so....

jamesj · Answer

Yes, a straight line.  Now, on that diagram, what is s?

anonymous · Answer

distance

jamesj · Answer

attachment

jamesj · Answer

The area under the velocity curve is the displacement, s, as indicated in the diagram I just posted.

Now, given that diagram, you will want to write down a formula for the area, s, as a function of u, v and a.

jamesj · Answer

You already know that you want v^2 - u^2 = 2as, hence it must be that
$$ s =\frac{v^2 - u^2}{2a}$$
You will need to convince yourself that that is correct.

jamesj · Answer

Hint, because a = (v-u)/t, we also know that t = (v-u)/a.

anonymous · Answer

u sure that it was right..??????

anonymous · Answer

????????????????

jamesj · Answer

Absolutely.  What is the formula for the area under that curve, just working from first principles?

jamesj · Answer

Consider it as a rectangle and a triangle.

anonymous · Answer

half*b*h

jamesj · Answer

I'm going to post one more diagram for you ... one sec

anonymous · Answer

okk

jamesj · Answer

The area under the curve has two parts: a rectangle and a triangle.  We build up the area of the total by finding the area of each piece. That is clearly indicated on this diagram.

anonymous · Answer

confused....

jamesj · Answer

What are you confused about?